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When you heat popcorn, it pops because it loses water explosively. Assume a kernel of corn, with a mass of \(0.125 \mathrm{g},\) has a mass of only \(0.106 \mathrm{g}\) after popping. (a) What percentage of its mass did the kernel lose on popping? (b) Popcorn is sold by the pound in the United States. Using \(0.125 \mathrm{g}\) as the average mass of a popcorn kernel, how many kernels are there in a pound of popcorn? \((1 \mathrm{lb}=453.6 \mathrm{g} .)\)

Short Answer

Expert verified
(a) Kernel loses 15.2% of its mass. (b) There are 3629 kernels in a pound of popcorn.

Step by step solution

01

Find Initial and Final Mass

The initial mass of the kernel is given as \(0.125\,\text{g}\) and the final mass after popping is \(0.106\,\text{g}\). We will use these values to calculate the mass lost.
02

Calculate Mass Lost

Subtract the final mass from the initial mass to find the mass lost: \(0.125\,\text{g} - 0.106\,\text{g} = 0.019\,\text{g}\).
03

Calculate Percentage Mass Lost

To find the percentage of mass lost, use the formula:\[\text{Percentage Loss} = \left( \frac{\text{Mass Lost}}{\text{Initial Mass}} \right) \times 100\%\]Substitute the values:\[\text{Percentage Loss} = \left( \frac{0.019\,\text{g}}{0.125\,\text{g}} \right) \times 100\% \approx 15.2\%\]
04

Calculate Kernels per Pound

To find out how many kernels are in a pound, divide the total mass in grams by the mass of one kernel:\[\text{Number of Kernels} = \frac{453.6\,\text{g}}{0.125\,\text{g}} = 3628.8\]Since you cannot have a fraction of a kernel, round this number to the nearest whole number.
05

Round the Number of Kernels

After rounding the previous result, there are 3629 kernels in a pound of popcorn.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Mass Percentage
Mass percentage is a way to express how much of one component is present in a mixture or compound compared to the whole, often as a percentage. When dealing with popcorn, calculating the mass percentage of water lost during popping gives insights into how much mass is lost due to water evaporation. To find this, we first need to determine the mass lost during popping, which is the difference between the initial and final mass of a popcorn kernel.
  • The initial mass is given as 0.125 g.
  • The mass after popping is 0.106 g.
  • The mass lost is 0.125 g - 0.106 g = 0.019 g.

The percentage of mass lost is calculated by dividing the mass lost (0.019 g) by the initial mass (0.125 g) and then multiplying by 100%. This results in a mass percentage loss of approximately 15.2%. It's important because it helps quantify changes in mass during chemical processes.
Unit Conversion
Unit conversion is essential in chemistry for expressing measurements in different units to make calculations consistent and convenient. In this exercise, we need to understand how to convert pounds to grams, as popcorn is often sold in pounds while calculations are performed in grams.
  • 1 pound (lb) is equal to 453.6 grams (g).

This conversion factor is crucial when calculating the number of popcorn kernels in a pound. Say you're given the mass of a kernel in grams, and you want to express that in terms of how many kernels there are in a pound. By converting the weight of a pound to grams, calculations become straightforward, helping understand the scale of popcorn amounts.
Mass in Grams
Mass in grams is a familiar unit of measurement in chemistry, often used due to its compatibility with the metric system and precision. Here, the mass of a popcorn kernel before and after popping is given in grams (0.125 g and 0.106 g, respectively). These values are crucial for calculating how much mass is lost due to popping.

Additionally, when determining how many kernels fit into a pound, knowing the mass of a single kernel in grams allows for division by the pound's equivalent mass in grams, providing a straightforward manner to calculate the number of kernels. This is because grams offer a common ground for comparing and calculating with other measurements in the metric system.
Chemical Processes
Chemical processes often involve changes in matter and energy, like when heating causes water to evaporate from popcorn, resulting in its popping. During these processes, matter can change form or location but is neither created nor destroyed—a principle known as the conservation of mass.

In this case, heating the popcorn initiates a process where water inside the kernel turns into steam. The expanding steam eventually causes the kernel to burst open. The resultant mass loss is primarily due to the evaporation of water, a physical change facilitated by the input of heat. Understanding this helps explain why the mass of the popcorn kernel decreases and why this is categorized as a chemical process, as it involves a change in the states of matter.

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Most popular questions from this chapter

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